Question

One year​ ago, your company purchased a machine used in manufacturing for $110,000. You have learned that a new machine is available that offers many​advantages; you can purchase it for $140,000 today. It will be depreciated on a​ straight-line basis over ten​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of $55,000 per year for the next ten years. The current machine is expected to produce EBITDA of $22,000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is $10,000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your​ company's tax rate is 38%​, and the opportunity cost of capital for this type of equipment is 11%. Is it profitable to replace the​ year-old machine?

The NPV of the replacement is ​$_________ (Round to the nearest​ dollar.)

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	31000
Tax shield on existing asset book value	=Book value * tax rate	38000
Cost of new machine		140000
=Initial Investment outlay		209000
Incremental EBIDTA=	55000-22000=		33000	33000	33000	33000	33000	33000	33000	33000	33000	33000
-Depreciation	Cost of equipment/no. of years		14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
=Pretax cash flows			47000	47000	47000	47000	47000	47000	47000	47000	47000	47000
-taxes	=(Pretax cash flows)*(1-tax)		29140	29140	29140	29140	29140	29140	29140	29140	29140	29140
+Depreciation			-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000
=after tax operating cash flow			15140	15140	15140	15140	15140	15140	15140	15140	15140	15140
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		209000	15140	15140	15140	15140	15140	15140	15140	15140	15140	15140
Discount factor=	(1+discount rate)^corresponding period	1	1.11	1.2321	1.367631	1.5180704	1.6850582	1.8704146	2.07616	2.30454	2.558037	2.839421
Discounted CF=	Cashflow/discount factor	209000	13639.63964	12287.96364	11070.238	9973.1869	8984.8531	8094.4623	7292.308	6569.65	5918.601	5332.073
NPV=	Sum of discounted CF=	298162.973